Geminiviruses are DNA viruses that infect several economically important crops, resulting in a reduction in their overall yield. These plant viruses have circular, single-stranded DNA genomes that replicate mainly by a rolling-circle mechanism. Geminivirus infection results in crosstalk between viral and cellular factors to complete the viral life cycle or counteract the infection as part of defense mechanisms of host plants. The geminiviral replication initiator protein Rep is the only essential viral factor required for replication. It is multifunctional and is known to interact with a number of host factors to modulate the cellular environment or to function as a part of the replication machinery. This review provides a holistic view of the research related to the viral Rep protein and various host factors involved in geminiviral DNA replication. Studies on the promiscuous nature of geminiviral satellite DNAs are also reviewed.